D-instantons in real time dynamics

Abstract

An instanton is known to exist in Euclidean spacetime only. Their role in real time dynamics is usually understood as a tunneling effect by Wick rotation. We illustrate other effects of instanton in holography by investigating five-dimensional effective gravity theory of the black D3-brane-D-instanton system. The supergravity description of the D3-brane-D-instanton system is dual to the super-Yang-Mills theory with topological excitations of the vacuum. We obtain Euclidean correlators in the presence of instantons by analyzing the fluctuations of the bulk fields in the five-dimensional effective theory. Furthermore, analytic continuation of Euclidean correlators leads to retarded correlators, which characterize real time dynamics. We find interestingly real time fluctuations of topological charge can destroy instantons and the lifetime of instanton is set by temperature. This implies instanton contribution to "real time dynamics" is suppressed at high temperature, which is analogous to classic field theory results that the instanton contribution to "thermodynamics" is suppressed at high temperature.